RESUMEN: Collective excitation modes of a diverse group of structures that show extreme two-dimensional properties are probed by inelastic light scattering methods. This talk presents an overview of recent results that reveal physics that is not accessible by other methods. Graphene, a single atomic layer of carbon arranged in a honeycomb lattice, is studied by Raman scattering measurements of the long wavelength optical phonon (the G-band). Gate-modulated low-temperature Raman spectra reveal that an external electric-field-effect (EFE) has marked impacts on the G-band of graphene by creating large density modulations of mass-less carriers with linear dispersion (known as Dirac fermions). The changes of phonon frequency and line-width demonstrate optically a particle-hole symmetry about the charge-neutral `Dirac-point'. Quantum Hall liquids of electrons in GaAs structures of high perfection are investigated by measurements of low-lying collective excitation modes using light scattering methods at miliKelvin temperatures. The light scattering experiments access directly low-lying "quasiparticle" excitations above the fluid ground states. These are the excitations that express distinct quantum phases of the electron liquids.